on the home page, it says "Take over the portal and build your own hive" but how exactly do I do that to get a throdama? I've also heard that symhurgs (spelling?) also can't be obtained that easily, is that true? And if it is, how can I get one? Thanks in advance :)

Take over the portal means the Battlefield http://beastkeeper.com/masscombat (Battles -> Battlefield). If you manage to hold the Portal in the middle of the map for 10 hours, you get a Throdama or Symurgh. So yes, getting one isn't an easy task. Your best bet is probably buying one off other people in the Pet Trades. 

thanks! I'm trying to train my pets up to lvl. 50 so wish me luck! :D